Freezing Point Depression

There are an uncountable number of news sites and news aggregators and people blogging about science news. This blog will not be about anything new. Instead I have decided to write about the things that I write about and talk about every day as a science educator. When I explain things to students I am filling out and adding on to what they’ve read in their text book or in their handout. Why not publish some of that material? So here’s to it.

The title of this post out of context is ambiguous. At least, it is to me. Disclosure: I have a pathological inability to avoid mentioning a pun when I notice one. To clear things up for readers who may have a similar pathology, this post is not about a clinically verified sadness due to having spent too much time in a Chemistry class talking about solid-liquid phase equilibrium.

Those of us who live in climates far enough from the equator to experience regular bouts of freezing precipitation are familiar with one of the ways we cope with ice. We spread salt on it, wait for it to get brittle and melt a bit, then we scrape it away. But why does the salt make the ice melt? On a dark night in February (at about 6:30 pm) I was outside spreading salt on the inch-thick slush and ice on my driveway when my five-year-old son asked me why the salt melts the ice. Even as a teacher with years of experience teaching students about this I was at a loss. How do I explain this in a way that a five-year-old can understand? Ultimately, I had to tell him that the salt makes the ice prefer to be a liquid rather than a solid. I wasn’t satisfied with this and neither was he but it was the best I could do. Now, I don’t think I can do any better than that to explain the situation to someone as young as five but I thought it would be interesting to try to explain it to a well-educated audience. Recently, I had to discuss this very topic with my AP Chemistry class and the following discussion is the result of my attempts to explain it to them. There are two ways to think about why spreading salt on ice makes it melt faster. One involves the way that particles act collectively to change the melting point temperature. The other (to be published separately) invokes the idea of entropy, a measurement of the amount of disorder, to explain the melting.

When chemists talk about freezing point depression it is as one of several so-called colligative properties. These properties of mixtures are ones that depend only on the number of particles and not on what they are. Salt works well to melt ice but sugar would work also, though not as well. This has to do with the number of particles you get when you dissolve these substances in water. When salt dissolves it makes two particles: one sodium ion and one chloride ion. When sugar dissolves it produces just one particle: a sugar molecule. So salt is twice as effective as sugar because it makes twice as many particles. Sugar has other disadvantages compared to salt. It’s sticky and leads to tooth decay.

Before I begin to explain how salt causes water to change from one phase of matter to another I’d like to describe how different phases of matter appear at the molecular level. In the solid phase molecules are stuck in place and can’t move except to vibrate a bit. In the liquid phase they are free to move around. When molecules are in the gas phase they are moving very fast and are not in contact with one another at all.

Ice is less dense than liquid water because its crystalline shape has big empty holes. All of the molecules are pinned in place.

This is a representation of water in the liquid phase. The molecules are stuck together by mutual attraction but move about freely.

This is a representation of water in the gas phase. All of the molecules are far apart and moving very rapidly.

Temperature and forces of attraction are the key to understanding the differences between the phases of matter. If the temperature is high, the molecules move faster. If the temperature is low, they move more slowly. All molecules attract other molecules with a tiny amount of force. If molecules are moving quickly enough they can break free of these attractive forces completely and zip around through empty space as a gas. If the molecules are moving more slowly then the forces of attraction keep them from careening off through space and they stay close together but remain mobile. If the molecules slow down even more then the forces of attraction force them to stay in place and a crystal forms. One place to explore these concepts is at the web site of the fine folks of the PhET project at the University of Colorado. Their State of Matter Java simulator rewards your time spent playing with it and can help you to build your understanding of how matter acts at the molecular scale. Find it here: http://phet.colorado.edu/en/simulation/states-of-matter-basics

If you looked extremely closely at the surface of a piece of ice you would find that molecules of water are constantly moving back and forth from the solid to the liquid phase. At a given temperature an equilibrium is set up so that the number of molecules sticking equals the number of molecules coming loose. At colder temperatures both rates are slower. Probably there is some temperature below which effectively no molecules are in the liquid phase but this is probably not common in places where people live.

When salt is spread on ice, even ice colder than the normal melting point, it dissolves in a thin surface layer of liquid water. The ions that make up the salt separate and act like particles of a liquid. This is when they are able to have an effect on the ice. Prior to the arrival of the salt ions, the water molecules were at their own equilibrium. The rate of sticking equaled the rate of coming loose. But now the water molecules in the liquid phase have company. For every hundred times a particle in the liquid phase hits the surface only a few are moving slowly enough to stick and become part of the ice. Let’s say 10 of the hundred move slowly enough to stick when they get near their brethren in the solid phase. Now for every hundred times a particle in the liquid phase strikes the surface of the ice only a fraction of them are even water molecules. For the sake of argument, let’s say that there are 10 salt particles and 90 water molecules for every hundred collisions. Salt ions do not become part of the solid ice. If 10 out of 100 water molecules stick when there are no salt ions then when only 90 water molecules hit the surface, only 9 are moving slowly enough to stick. This results in a reduction in the rate of sticking while the rate of coming loose remains the same.

So the situation is one of competing rates. On the one hand we have the rate of sticking–the number of molecules that stick per second might be one way to express it. Let’s call this the freezing rate. On the other hand we have the rate of coming loose–the number of molecules that come loose per second. This is the melting rate. At the normal melting point with no salt these rates equal one another and there is no change in the total amount of ice over time. Once salt is spread over the surface of the ice the freezing rate slows down relative to the melting rate. As long as the temperature remains unchanged we can imagine water molecules merrily breaking their bonds with their crystalline neighbors and bouncing away up among their liquid friends. The tired, slow molecules jostled by their liquid neighbors don’t have as many opportunities to settle down to rest. Like an exhausted parent, there is always one more thing to do before you can finally lie down. This asymmetry leads to a net change in the amount of ice: it decreases while the amount of liquid increases. That is why ice melts when you put salt on it.

On some other day I will explain why the ice not only melts when the salt is strewn on it but also gets colder.

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[…] this mixture has a freezing point below the normal freezing point for water, which is 0°C. (See my other post about why ice melts when salt is poured on it.) In order to make a dessert that is a treat to eat […]